oliadas73

oliadas73

Answered

2022-10-09

Making sense of this formula relating to polynomials :
P ( x + n + 1 ) = i = 0 n ( 1 ) n 1 ( n + 1 i ) P ( x + i )

Do you have a similar question?

Recalculate according to your conditions!

Answer & Explanation

lascosasdeali3v

lascosasdeali3v

Expert

2022-10-10Added 10 answers

"If you take the right side over to the left (correcting a minor typo - ""n-1"" should be ""n-i"" in the power of -1), the equation can also be written like this:
i = 0 n + 1 1 n + 1 i n + 1 i P x + i = 0
What this is, is actually the iterated difference. That is, if Δ f 0 = f 1 f 0 , and Δ 2 f 0 = Δ f 1 f 0 = f 2 2 f 1 + f 0 Δ n + 1 P x = 0
And if our polynomial is of order n or lower, then this must be true. To see this, consider that, for P x = x n , we have
Δ x n = x + 1 n x n = k = 0 n 1 n k x k
And
Δ C = 0
for any constant C. So, iterating the Δ operation n + 1 times, you end up with Δ n + 1 x n = 0"

Still Have Questions?

Ask Your Question

Free Math Solver

Help you to address certain mathematical problems

Try Free Math SolverMath Solver Robot

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?